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Automatic intervalwise block partitioning using Adams type method and backward differentiation formula for solving ODEs

Most methods for solving stiff systems of ordinary differential equations (ODEs) are based on backward differentiation formulas (BDFs) which normally require repeated solution of systems of linear equations with coefficient matrix, IhbJ,where J is the Jacobian matrix as part of a Newton-like iterati...

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Main Authors: Othman, Khairil Iskandar, Ibrahim, Zarina Bibi, Suleiman, Mohamed, Majid, Zanariah
格式: Article
語言:English
出版: Elsevier 2007
在線閱讀:http://psasir.upm.edu.my/id/eprint/7668/
http://dx.doi.org/10.1016/j.amc.2006.11.020
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spelling my.upm.eprints.76682014-04-18T05:11:21Z http://psasir.upm.edu.my/id/eprint/7668/ Automatic intervalwise block partitioning using Adams type method and backward differentiation formula for solving ODEs Othman, Khairil Iskandar Ibrahim, Zarina Bibi Suleiman, Mohamed Majid, Zanariah Most methods for solving stiff systems of ordinary differential equations (ODEs) are based on backward differentiation formulas (BDFs) which normally require repeated solution of systems of linear equations with coefficient matrix, IhbJ,where J is the Jacobian matrix as part of a Newton-like iteration on each time step. The matrix operations in the iteration scheme consumes a considerable amount of computational effort. Therefore, in this paper, our objective is to reduce the cost of the iteration scheme by technique of partitioning. The strategy adopted for partitioning is based on block Adams method and block BDF method. Numerical results demonstrates the efficiency of the proposed partitioning in improving both the accuracy and CPU time over traditional stiff methods. Elsevier 2007 Article PeerReviewed Othman, Khairil Iskandar and Ibrahim, Zarina Bibi and Suleiman, Mohamed and Majid, Zanariah (2007) Automatic intervalwise block partitioning using Adams type method and backward differentiation formula for solving ODEs. Applied Mathematics and Computation, 188 (1). pp. 1642-1646. ISSN 0096-3003 http://dx.doi.org/10.1016/j.amc.2006.11.020 10.1016/j.amc.2006.11.020 English
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description Most methods for solving stiff systems of ordinary differential equations (ODEs) are based on backward differentiation formulas (BDFs) which normally require repeated solution of systems of linear equations with coefficient matrix, IhbJ,where J is the Jacobian matrix as part of a Newton-like iteration on each time step. The matrix operations in the iteration scheme consumes a considerable amount of computational effort. Therefore, in this paper, our objective is to reduce the cost of the iteration scheme by technique of partitioning. The strategy adopted for partitioning is based on block Adams method and block BDF method. Numerical results demonstrates the efficiency of the proposed partitioning in improving both the accuracy and CPU time over traditional stiff methods.
format Article
author Othman, Khairil Iskandar
Ibrahim, Zarina Bibi
Suleiman, Mohamed
Majid, Zanariah
spellingShingle Othman, Khairil Iskandar
Ibrahim, Zarina Bibi
Suleiman, Mohamed
Majid, Zanariah
Automatic intervalwise block partitioning using Adams type method and backward differentiation formula for solving ODEs
author_facet Othman, Khairil Iskandar
Ibrahim, Zarina Bibi
Suleiman, Mohamed
Majid, Zanariah
author_sort Othman, Khairil Iskandar
title Automatic intervalwise block partitioning using Adams type method and backward differentiation formula for solving ODEs
title_short Automatic intervalwise block partitioning using Adams type method and backward differentiation formula for solving ODEs
title_full Automatic intervalwise block partitioning using Adams type method and backward differentiation formula for solving ODEs
title_fullStr Automatic intervalwise block partitioning using Adams type method and backward differentiation formula for solving ODEs
title_full_unstemmed Automatic intervalwise block partitioning using Adams type method and backward differentiation formula for solving ODEs
title_sort automatic intervalwise block partitioning using adams type method and backward differentiation formula for solving odes
publisher Elsevier
publishDate 2007
url http://psasir.upm.edu.my/id/eprint/7668/
http://dx.doi.org/10.1016/j.amc.2006.11.020
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score 13.250246

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